Term of Award

Spring 2024

Degree Name

Master of Science in Mathematics (M.S.)

Document Type and Release Option

Thesis (open access)

Copyright Statement / License for Reuse

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.


Department of Mathematical Sciences

Committee Chair

Hua Wang

Committee Member 1

Sungkon Chang

Committee Member 2

Daniel Gray


In the first part of this work we introduce a variation of the well-known Ramsey number, which we call the Exact Ramsey Number (ERN) or Strong Ramsey Number (STN). The ERN of $s$ and $t$, denoted by $\mathcal{R}(s,t)$, is defined as the minimum $\ell$ such that any two colouring of $K_{\ell}$ that does not contain monochromatic $K_{s+1}$ of the first colour or monochromatic $K_{t+1}$ of the second colour must contain a monochromatic $K_s$ of the first colour and a monochromatic $K_t$ of the second colour. We establish some properties of these ERNs, including the evaluation of small ERNs and generalizations of well-known theories of the classic Ramsey numbers. We also study the relation between the ERN and the classic Ramsey numbers.

The second part of this work is on the Middle Levels Problem. The middle level conjecture is about the presence of a Hamiltonian cycle in the middle layer graph of a hypercube. In this work we give a new approach to the Middle Levels Problem. This approach can also be extended to the Central Levels Problem.

OCLC Number


Research Data and Supplementary Material


Available for download on Thursday, April 19, 2029